ELEMENTARY STATISTICAL METHODS

1. ELEMENTARY STATISTICAL METHODS Dr. ReshmaReghu Lecturer Dept of Community Medicine

2. PRIMARY DATA • Data that is obtained directly from an individual is called primary data. • The census of 1991 is an example of collecting primary data relating to the population. • Primary data gives the precise information wanted

3. SECONDARY DATA • Data that is obtained from outside source is called secondary data. • If we are studying the hospital records. and want to use the census data, the census data becomes secondary data.

4. Presentation of Statistical Data Statistical data, once collected, must be arranged purposively, in order to bring out the important points clearly and strikingly. Therefore the manner in which statistical data is presented is of utmost importance. There are several methods of presenting data- tables, charts, diagrams, graphs, pictures and special curves.

5. TABULATION Tables are devices for presenting data simply from masses of statistical data. Tabulation is the first step before the data is used for analysis or interpretation. A table can be simple or complex, depending upon the number or measurement of a single set or multiple sets of items.

6. General principles in designing tables • The tables should be numbered e.g., Table 1, Table 2, etc. (b) A title must be given to each table. The title must be brief and self explanatory. (c) The headings of columns or rows should be clear and concise. (d) The data must be presented according to size or importance; chronologically, alphabetically or geographically,. (e) If percentages or averages are to be compared, they should be placed as close as possible. (f) No table should be too large. (g) Most people find a vertical arrangement better than a horizontal one because, it is easier to scan the data from top to bottom than from left to right,. (h) Foot notes may be given, where necessary, providing explanatory notes or additional information.

7. TYPES • Simple Tables • Frequency Distribution Table

9. Frequency Distribution Table • In a frequency distribution table, the data is first split up into convenient groups (class intervals) and the number of items (frequency) which occur in each group is shown in the adjacent column. • As a practical rule, it might be stated that when there is large data, a maximum of 20 groups, and when there is not much data, a minimum of 5 groups, could be conveniently taken. • As far as possible, the class intervals should be equal, so that observations could be compared. • The merits of a frequency distribution table are, that it shows at a glance how many individual observations are in a group, and where the main concentration lies. • It also shows the range, and the shape of distribution. ·

11. CHARTS AND DIAGRAMS • Charts and diagrams are useful methods of presenting simple statistical data. They have a powerful impact on the imagination of people. Therefore, they are a popular media of expressing statistical data, especially in newspapers and magazines. The impact of the picture depends on the way it is drawn.

12. Few remarks • Diagrams are better retained in the memory than statistical tables. • The data that is to be presented by diagrams ought to be simple. • Then there is no risk that the reader will misunderstand. However, simplicity may be obtained only at the expense of details and accuracy. That is, lot of details of the original data may be lost in the charts and diagrams. If we want the real study, we have to go back to the original data.

13. Bar charts • They are diagrams of Qualitative Data • Usually prefered for scientific presentation • Bar charts are merely a way of presenting a set of numbers by the length of a bar, the length of the bar is proportional to the magnitude to be represented. • Bar charts are a popular media of presenting statistical data because they are easy to prepare, and enable values to be compared visually.

14. SIMPLE BAR CHART • Bars may be vertical or horizontal. • The bars are usually separated by appropriate spaces with an eye to neatness and clear presentation. • A suitable scale must be chosen to present the length of the bars.

16. MULTIPLE BAR CHART • Two or more bars can be grouped

17. COMPONENT BAR CHART • The bars may be divided into two or more parts ... Each part representing a certain item and proportional to the magnitude of that particular item.

18. HISTOGRAM • It is a pictorial diagram of frequency distribution. • It consists of a series of blocks. • The class intervals are given along the horizontal axis and the frequencies along the vertical axis. • The area of each block or rectangle is proportional to the frequency. • Diagramatic representation of quantitative data

20. FREQUENCY POLYGON • A frequency distribution may also be represented diagrammatically by the frequency polygon. • It is obtained by joining the mid-points of the histogram blocks.

21. LINE DIAGRAM • Line diagrams are used to show the trend of events with the passage of time.

22. PIE CHART • Instead of comparing the length of a bar, the areas of segments of a circle are compared. • The area of each segment depends upon the angle. • Pie charts are extremely popular with the laity, but not with statisticians who consider them inferior to bar charts. • It is often necessary to indicate the percentages in the segments as it may not be sometimes very easy, virtually, to compare the areas of segments.

24. PICTOGRAMS • Pictograms are a popular method of presenting data to the "man in the street" and to those who cannot understand orthodox charts. • Small pictures or symbols are used to present the data. For example, a picture of doctor to represent the population per physician. • Fractions of the picture can be used to represent numbers smaller than the value of a whole symbol. • In essence, pictograms are a form of bar charts. ·

26. STATISTICAL MAPS • When statistical data refer to geographic or administrative areas, it is presented either as "Shaded Maps“ or "Dot maps" according to suitability. • The shaded maps are used to present data of varying size. The areas are shaded with different colours, or different intensities of the same colour, which is indicated in the key. • Scatter diagram shows the relationship between two variables,

27. SPOTTED MAPS & SCATTER DIAGRAMS

28. STATISTICAL AVERAGES • The word "average" implies a value in the distribution, around which the other values are distributed. • Commonly used are : - (1) The Arithmetic Mean (2) Median and (3) The Mode

29. MEAN • The arithmetic mean is widely used in statistical calculation. It is sometimes simply called Mean. • To obtain the mean, the individual observations are first added together, and then divided by the number of observations. • The operation of adding together is called 'summation' and is denoted by the sign Σ or S. • The individual observation is denoted by the sign ŋ and the mean is denoted by the sign X(called "X bar").

30. The advantages of the mean are that it is easy to calculate and understand. • The disadvantages are that sometimes it may be unduly influenced by abnormal values in the distribution.

31. MEDIAN • The median is an average of a different kind, which does not depend upon the total and number of items. • To obtain the median, the data is first arranged in an ascending or descending order of magnitude, and then the value of the middle observation is located, which is called the median.

32. MODE • The mode is the commonly occurring value in a distribution of data. It is the most frequent item or the most "fashionable" value in a series of observations. • For example, the diastolic blood pressure of 20 individuals was : 85, 75,81, 79, 71,95, 75, 77, 75,90, 71, 75, 79,95, 75, 77,84, 75,81, 75 • The mode or the most frequently occurring value is 75.

33. The advantages of mode are that it is easy to understand, and is not affected by the extreme items. • The disadvantages are that the exact location is often uncertain and is often not clearly defined. • Therefore, mode is not often used in biological or medical statistics.

34. MEASURES OF DISPERSION • There are several measures of variation (or "dispersion“ as it is technically called) of which the following are widely known: (a) The Range (b) The Mean or Average Deviation (c) The Standard Deviation

35. RANGE • The range is by far the simplest measure of dispersion. It is defined as the difference between the highest and lowest figures. • It indicates only the extreme values between the two values and nothing about the dispersion of values between the two extreme values.

36. MEAN DEVIATION • It is the average of the deviations from the arithmetic mean.

38. The Standard Deviation • The standard deviation is the most frequently used measure of deviation. In simple terms, it is defined as "Root Means Square Deviation.“ • It is denoted by the Greek letter sigma or by the initials S.D.

39. When the sample size is more than 30

40. When the sample size is less than 30

41. NORMAL DISTRIBUTION • The normal distribution or 'normal curve' is an important concept in statistical theory. • Theshape of the curve will depend upon the mean and standard deviation which in turn will depend upon the number and nature of observations. • It is useful to note at this stage that in a normal curve (a). the area between one standard deviation on either side of the mean ( x ± 1 S.D ) will include approximately 68 per cent of the values in the distribution, (b) the area between two standard deviations on either side of the mean ( x ± 2 S.D ) will cover most of the values, i.e., approximately 95 per cent of the values, and (c) the area between ( x ± 3 S.D ) will include 99. 7 per cent of the values. These limits on either side of the mean are called "confidence limits"

42. NORMAL CURVE

45. SAMPLING • The process of selecting a representative part from the whole is called Sampling. • The whole from which the sample is drawn is called Population • The whole may be finite or infinite. So it is denoted as Universe

46. SAMPLING FRAME • A sampling frame is a listing of the members of the universe from which the sample is to be drawn. The accuracy and completeness of the sampling frame influences the quality of the sample drawn from it.

47. SAMPLING METHODS • Simple Random Sampling • Systematic Random sampling • Stratified Random Sampling

48. ERRORS • Sampling Errors The variation in the result of one sample to another is Sampling Error. It is inherent to the sampling procedure. • Factors that influence the Sampling Error • Size of the sample • Natural variability of the individual reading

49. Non- Sampling Error • Errors may occur due to inadequately calibrated instruments, due to observer variation as well as due to incomplete coverage in examining the subjects selected and conceptual errors. • These are often more important than sampling errors.

50. Standard Error • S. E is defined as the Standard deviation of repeated sample means or proportions taken from same population. • It is a very effective standard deviation which is close to the true value of the population. • It is the fundamental tool used in Statistics for estimation and tests of significance.